Radars are widely used for motor vehicles. Specifically, such a radar installed in a motor vehicle works to emit radio waves from a transmitting antenna, receive, by a receiving antenna array, echoes reflected from targets. The receiving antenna array consists of a plurality of antennas in array.
The radar works to analyze the received echoes to thereby estimate the range to each target, the azimuth direction of each target with respect to the radar, and/or a relative speed between each target and the motor vehicle.
Specifically, the radar estimates the range to each target based on the time difference (delay) between the arrival of each echo and a corresponding transmitted radio wave. The radar also estimates the relative speed between each target and the radar based on the doppler shift in each echo with respect to a corresponding transmitted radio wave.
In addition, the radar estimates the direction of each target in azimuth based on the differences in phase among the echoes received by the antennal elements of the antenna array; these differences in phase among the echoes depend on their directions of arrival.
The MUSIC (Multiple Signal Classification) method, one of various methods for estimating the direction of a target in azimuth using a receiving antenna array, is frequently used. For example, the MUSIC method is disclosed in Japanese Patent Application Publications 2006-047282 and 2000-121716 and in Toshiyuki NAKAZAWA et al, “Estimating Angle of Arrival with Non-uniformly Spaced Array: IEICE Transactions on Information and Systems, “Vol. J83-B”, “No. 6”, “pp. 845-851”. The literature of “Estimating Angle of Arrival with Non-uniformly Spaced Array” will be referred to as “nonpatent document” hereinafter.
The summary of the MUSIC method will be described hereinafter assuming that the antenna array consists of K antennas arranged in a linear array. For example, reference numeral 19 in FIG. 1 represents such an antenna array.
A signal of each of the K antennas based on arrival echoes received by the K antennas defines a received vector X as the following equation (1), and, from the equation (1), an autocorrelation mat Rxx with K rows and K columns represented as the following equation (2) is derived:
                              X          ⁡                      (            i            )                          =                              [                                                            x                  1                                ⁡                                  (                  i                  )                                            ,                                                x                  2                                ⁡                                  (                  i                  )                                            ,              …              ⁢                                                          ,                                                x                  k                                ⁡                                  (                  i                  )                                                      ]                    T                                    (        1        )                                Rxx        =                              1            L                    ⁢                                    ∑                              i                =                1                            L                        ⁢                                          X                ⁡                                  (                  i                  )                                            ⁢                                                X                  H                                ⁡                                  (                  i                  )                                                                                        (        2        )            
where T represents transpose of vector, H represents transpose of complex conjugate, xk(i) as an element of the received vector X(i) (k=1, 2, . . . , K) represents a value of the received signal of a k-th antenna at time i, and L represents the number of snapshots (samples) of the received vector X(i).
Specifically, the autocorrelation matrix Rxx is derived from the L snapshots of the received vector xk(i).
Thereafter, K eigenvalues λ1, λ2, . . . , λK of the autocorrelation matrix Rxx are obtained to meet the equation “λ1≧λ2≧ . . . ≧λK”. A number M of arrival echoes is estimated in accordance with the following equation (2a):λ1≧λ2≧ . . . ≧λM>λth≧λM+1= . . . =λK  (2a)
where λth represents a threshold corresponding to thermal noise power σ2. Note that a real value of the thermal noise power σ2 is unclear, and therefore, the threshold λth can be used as the thermal noise power σ2. The average value of the eigenvalues λM+1, λM+2, . . . , λM+K can be used in place of the threshold λth.
In addition, (K−M) eigenvectors eM+1, eM+2, . . . eK corresponding to the (K−M) eigenvalues λM+1, λM+2, . . . , λK are calculated. The (K−M) eigenvectors eM+1, eM+2, . . . eK will be referred to as “noise eigenvector EN” hereinafter (see the following equation (3)):EN=(eM+1,eM+2, . . . , eK)  (3)
When a complex response vector of the antenna array with respect to an azimuth parameter θ is defined as a steering vector α(θ) the following equation (3a) is established:αH(θ)EN=0  (3a)
Note that the azimuth parameter θ represents an incident angle of an arrival echo with respect to a direction orthogonal to the receiving surface of the antenna array.
The equation (3a) represents that the noise eigenvector EN is orthogonal to the steering vector α(θ) when the steering vector α(θ) is directed to the azimuth of the arrival echoes.
From the equation (3a), a MUSIC spectrum, which is defined as “performance function PMN” given by the following equation (4), is derived:
                              P          MN                =                                            1                                                ∑                                      i                    =                                          M                      +                      1                                                        K                                ⁢                                                                                                                        e                        i                        H                                            ⁢                                              a                        ⁡                                                  (                          θ                          )                                                                                                                          2                                                      ×                                          a                H                            ⁡                              (                θ                )                                      ⁢                          a              ⁡                              (                θ                )                                              ⁢                                          ⁢                                          =                                                                      a                                      H                    ⁢                                                                                                                ⁡                                  (                  θ                  )                                            ⁢                              a                ⁡                                  (                  θ                  )                                                                                                      a                  H                                ⁡                                  (                  θ                  )                                            ⁢                              E                N                            ⁢                              E                N                H                            ⁢                              a                ⁡                                  (                  θ                  )                                                                                        (        4        )            
The MUSIC spectrum defined by the equation (4) demonstrates that its shaper peaks at nulls appear when corresponding azimuths of the azimuth parameter θ are in agreement with the azimuths of the arrival echoes.
Thus, extraction of the peaks of the MUSIC spectrum obtains estimated azimuths θ1, . . . , θM of the arrival radio waves, that is, estimated azimuths of targets that cause the echoes.
Note that the extracted peaks may include peaks due to noise components in addition to peaks caused by the echoes.
Thus, in order to estimate, with high accuracy, the directions of targets in azimuth, the estimated azimuths θ1, . . . , θM of the arrival echoes extracted from the MUSIC spectrum are set as power estimation targets, and thereafter, received power levels P1, . . . , PM of the power estimation targets θ1, . . . , θM are calculated.
At least one of the power estimation targets θ1, . . . , θM, the received power level of which is equal to or greater than a threshold power level Pth, is estimated as the azimuth of at least one real target. The direction of a noise component has a lower received power level. For this reason, estimation, as the azimuth of at least one target, of at least one of the power estimation targets θ1, . . . , θM, the received power level of which is equal to or greater than the threshold power level Pth, reduces improper estimations of the azimuths of the targets due to the noise components.
Specifically, the estimation of the received power levels P1, . . . , PM of the power estimation targets θ1, . . . , θM will be carried out in accordance with the following steps.
First, a steering matrix A is generated based on the steering vectors α(θ1), . . . , α(θM) corresponding to the power estimation targets θ1, . . . , θM is generated (see the following equation (5)):A=[α(θ1),α(θ2), . . . , α(θM−1),α(θM)]  (5)
Based on the steering matrix A, a matrix S represented by the following equation (6) is calculated:S=(AHA)−1AH(Rxx−σ2I)A(AHA)−1  (6)
where I represents a unit matrix, and σ2 represents the thermal noise power.
From the m diagonal components in the equation (6), the received power levels Pm of the power estimation targets θm (m=1, 2, . . . , M) is derived (see the following equation (7)):[P1,P2, . . . , PM−1,PM]=diag(S)  (7)
where diag(f) represents the diagonal components of a given matrix f.
As described above, at least one of the power estimation targets θ1, . . . , θM, the received power level of which is equal to or greater than the threshold power level Pth, is estimated as the azimuth of at least one real target.
The estimation of the azimuths of targets based on the MUSIC method normally uses a receiving antenna array consisting of a plurality of uniformly spaced antennas; this type of antenna arrays will be referred to as ‘uniformly spaced antenna array’ hereinafter.
In the uniformly spaced antenna array using the MUSIC method set fort above, the difference of 2nπ (n is an integer) in phase between actual arrival echoes received by adjacent antennas cyclically causes grating lobes.
That is, a space spanned by steering vectors indicating given azimuths of actual arrival echoes with respect to the uniformly spaced antenna array include steering vectors indicating azimuths of the generated grating lobes.
Thus, it is necessary to determine a scanning azimuth range of the uniformly spaced antenna array so as to prevent detection of the grating lobes; this scanning azimuth range will be also referred to as “field of view (FOV)” hereinafter. In other words, it is necessary to uniformly narrow the spaces between adjacent antennas of the uniformly spaced antenna array. The narrowing of the antenna-array spaces widens the FOV of the uniformly spaced antenna array.
However, because the azimuth resolution of the uniformly spaced antenna array is determined by the length of the aperture thereof to maintain high the azimuth resolution of the uniformly spaced antenna array with the FOV being wide contributes to an increase in the number of antennas; this results in an increase in the cost of the uniformly spaced antenna array.
In addition, it may be difficult to narrow the spaces between adjacent antennas of the uniformly spaced antenna array because the narrowing causes the number of antennas and mutual coupling between the antennas to increase.
In view of the foregoing problems, the nonpatent document discloses a non-uniformly spaced antenna array consisting of a plurality of non-uniformly spaced antennas. The proper setting of non-uniform spaces between adjacent antennas of the non-uniformly spaced antenna array allows determination of whether a steering vector in a given azimuth with a required FOV under the estimated number of arrival echoes is included in spaces spanned by steering vectors indicating given azimuths of actual arrival echoes.
These non-uniformly spaced antenna arrays with a plurality of proper unequal spaced antennas, which employ the MUSIC method, increase its FOV as compared with uniformly spaced antenna arrays set forth above.
Specifically, the nonpatent document focuses on the linear independence between steering vectors A{α(θ1), . . . , α(θM)} corresponding to given azimuths θ1, . . . , θM and a given steering vector α(θS) with a required FOV. Guaranteeing the linear independence between the steering vectors A{α(θ1), . . . , α(θM)} and the steering vector α(θS) guarantees that the steering vector α(θS) is not included in the spaces spanned by the steering vectors indicating azimuths of actual arrival echoes when the number of the actual arrival echoes is equal to or lower than M.
When the linear independence between the arrival-azimuth steering vectors A{α(θ1), . . . , α(θM)} and the given steering vector α(θS) becomes low, the given steering vector α(θS) is represented by the following equation (7a):
                              a          ⁡                      (                          θ              S                        )                          =                                            ∑                              m                =                1                            M                        ⁢                                          c                m                            ⁢                              a                ⁡                                  (                                      θ                    m                                    )                                                              +          r                                    (                  7          ⁢          a                )            
where r represents a given vector (|r|≠0,|r|<<1), and cm is a given complex number.
The reduction in the linear independence between the arrival-azimuth steering vectors A{α(θ1), . . . , α(θM)} and the given steering vector α(θS) may cause peaks of the MUSIC spectrum to appear in azimuths θS corresponding to the steering vector α(θS).
Note that, in the specification, ambiguity peaks of the MUSIC spectrum that are not due to noise and are not caused by arrival echoes based on transmitted radio waves will be expressed as ‘undesired peaks’ hereinafter. In contrast, peas caused by arrival echoes based on transmitted radio waves will be referred to as “desired peaks” hereinafter.
In addition, the fact that the L2 norm of the vector r in the equation (6), expressed by “√{square root over (|r|2)}”, is lower than a preset value means that the linear independence between the arrival-azimuth steering vectors and given steering vectors is weak (low). Similarly, the fact that the L2 norm of the vector r in the equation (6) is higher than the preset value means that the linear independence between the arrival-azimuth steering vectors and the given steering vectors is strong (high).
More specifically, in radars equipped with such a non-uniformly spaced antenna array, not only appear desired peaks, but also appear peaks due to noise and undesired peaks. In these radars, the number M of arrival echoes is designed to be estimated, independently of the linear independence between the arrival-azimuth steering vectors and given steering vectors, with an accuracy identical to that obtained by radars equipped with a uniformly spaced antenna array.
Thus, in these radars equipped with a non-uniformly spaced antenna array, when azimuths of power estimation targets corresponding to the number M of the arrival echoes are selected form the MUSIC spectrum, azimuths corresponding to desired peaks may not be selected, but those corresponding to undesired peaks may be erroneously selected.
When a received power level of a power estimation target corresponding to an undesired peak is calculated set forth above, the calculated received power level may be high because of the weakness of the linearly independence between the arrival-azimuth steering vectors and given steering vectors.
For this reason, unlike the received power level of a power estimation target corresponding to a peak due to noise, the comparison between the received power level of a power estimation target corresponding to an undesired peak and the threshold power level Pth cannot eliminate the power estimation target corresponding to the undesired peak. This results in that azimuths in which there are no targets may be erroneously estimated as the azimuths of real targets.
For example, it is assumed that a MUSIC spectrum of received signals of a non-uniformly antenna array illustrated in FIG. 17A is obtained. The MUSIC spectrum has three peaks corresponding to three azimuths θ1, θ2, and θ3.
In this assumptions when no undesired peaks are contained in the MUSIC spectrum and the peak at the azimuth θ3 is due to noise, estimation of received power levels P1, P2, and P3 corresponding to the three azimuths θ1, θ2, and θ3 allows the azimuth θ3 due to noise to be definitely separated from the azimuths θ1 and θ2 of real targets. This is because the received power level P3 is clearly distinguished from the received power levels P1 and P2 based on the threshold power level Pth (see FIG. 17B).
In contrast, when one undesired peak at the azimuth θ3 is contained in the MUSIC spectrum, even if received power levels P1, P2, and P3 corresponding to the three azimuths θ1, θ2, and θ3 are estimated, it is difficult to separate the azimuth θ3 corresponding to the undesired peak from the azimuths θ1 and θ2 of real targets. This is because there are no clear differences between the received power levels P1 to P3 (see FIG. 17C).
In summary, conventional radars equipped with a non-uniformly spaced antenna array in place of a uniformly spaced antenna array may increase the possibility of erroneously estimating azimuths of targets due to undesired peaks, thus deteriorating the estimation accuracy of azimuths of targets.